Practical Finite Element Analysis for Mechanical Engineering

COVER
TITLE PAGE
COPYRIGHT PAGE
EBOOK DISCLAIMER
ACKNOWLEDGEMENTS
TABLE OF CONTENTS
TECHNICAL REVIEW COMMITTE
PREFACE
Chapter 1	DEFINING FINITE ELEMENT ANALYSIS
	1.1	OVERVIEW
	1.2	METHODS FOR SOLVING AN ENGINEERING PROBLEM
	1.3	THE DIFFERENT NUMERICAL METHODS
	1.4	INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS (PDEs)
	1.5	WHAT IS FINITE ELEMENT ANALYSIS (FEA)?
Chapter 2	WORKING WITH FEA
	2.1	FROM MATHEMATICS TO COMPUTER SCIENCE
	2.2	THE MAGIC OF DISCRETIZATION
	2.3	PRE-PROCESSING
	2.4	SOLVING
		2.4.1	DIRECT SOLVER
		2.4.2	ITERATIVE SOLVER
	2.5	POST-PROCESSING
	2.6	FEA PROCESS SUMMARY
	2.7	CAPABILITIES OF FEA SOFTWARE
	2.8	HOW ACCURATE IS FEA?
		2.8.1	CAD SIMPLIFICATION
		2.8.2	DISCRETIZATION
		2.8.3	MODELING OF THE JOINTS
		2.8.4	MATERIAL
		2.8.5	LOADING
		2.8.6	BOUNDARY CONDITIONS
		2.8.7	BEHAVIORS CAPTURED BY FEA
		2.8.8	CONCLUSION
	2.9	WHY DO FINITE ELEMENT ANALYSIS?
	2.10	HOW CAN FEA HELP YOU?
	2.11	WHAT IS NEEDED TO PERFORM AN FE SIMULATION?
Chapter 3	BECOMING AN FEA SPECIALIST
	3.1	OVERVIEW
	3.2	WHAT DO YOU NEED TO LEARN IN THE FEA FIELD?
	3.3	GUIDELINES FOR FEA LEARNING
	3.4	WHEEL OF STRUCTURAL FEA COMPETENCIES
	3.5	CONCLUSION
Chapter 4	HISTORY OF FEA
	4.1	THE PIONEERS
	4.2	FEA TIMELINE
Chapter 5	BASIS OF FINITE ELEMENT METHOD THEORY
	5.1	OVERVIEW
	5.2	THE EQUILIBRIUM EQUATION
	5.3	DISPLACEMENT METHOD
		5.3.1	THREE CONDITIONS
		5.3.2	STIFFNESS MATRIX
		5.3.3	LINEAR SPRING MODEL
		5.3.4	APPLICATION TO THE TWO-SPRING SYSTEM
		5.3.5	APPLICATION TO THE FOUR-SPRING SYSTEM
		5.3.6	APPLICATION TO A PARALLEL-SPRING SYSTEM
	5.4	PRINCIPLE OF MINIMUM POTENTIAL ENERGY
	5.5	ELEMENT STIFFNESS MATRIX FOR VARIOUS TOPOLOGIES
		5.5.1	OVERVIEW
		5.5.2	DEGREES OF FREEDOM
		5.5.3	SHAPE FUNCTIONS
		5.5.4	1D TRUSS ELEMENT
		5.5.5	1D BEAM ELEMENT
		5.5.6	2D ELEMENTS
		5.5.7	3D SOLID ELEMENT
	5.6	HOW IS THE STIFFNESS MATRIX ASSEMBLED?
		5.6.1	MATRIX ASSEMBLY
		5.6.2	TAKING ADVANTAGE OF SPARSITY AND SYMMETRY
		5.6.3	BANDED MATRIX
		5.6.4	SKYLINE MATRIX STORAGE
	5.7	HOW ARE FEM EQUATIONS SOLVED?
		5.7.1	DIRECT SOLUTION
		5.7.2	ITERATIVE SOLUTION
Chapter 6	DEFINING YOUR FEA STRATEGY
	6.1	OVERVIEW
	6.2	TIME
	6.3	THE 10 STEPS TO FOLLOW
	6.4	EXPOSE THE PROBLEM
	6.5	DEFINE THE GOALS
	6.6	ANALYZE THE HISTORY
	6.8	EVALUATE THE BOUNDARIES AND SURROUNDING ENVIRONMENT
	6.9	UNDERSTAND THE LOADING AND PREDICT THE LOAD PATH
	6.10	SELECT THE ELEMENT TYPES AND MODEL SIZE
	6.11	PREDICT THE FINAL RESULTS
	6.12	REVIEW THE PLAN
	6.13	14 QUESTIONS YOU SHOULD BE ABLE TO ANSWER BEFORE YOU BEGIN MODELING
	6.14	LARGE-SCALE MODELING TECHNIQUES
	6.15	CONCLUSION
Chapter 7	THE LIBRARY OF ELEMENTS
	7.1	OVERVIEW
	7.2	ELEMENT TYPES
		7.2.1	OVERVIEW
		7.2.2	1D ELEMENTS
		7.2.3	2D ELEMENTS
		7.2.4	3D ELEMENTS
		7.2.5	SPECIAL ELEMENTS
	7.3	ELEMENT SELECTION CRITERIA
		7.3.1	ELEMENT TYPE
		7.3.2	DEGREES OF FREEDOM
		7.3.4	COST
		7.3.5	ACCURACY
	7.4	HOW TO CHOOSE THE RIGHT ELEMENT
		7.4.1	PREDICT YOUR STRUCTURE’S BEHAVIOR
		7.4.2	EXPERIMENT YOUR LIBRARY OF ELEMENTS
		7.4.3	GEOMETRY SIZE AND SHAPE
		7.4.4	ELEMENT ORDER: LINEAR OR QUADRATIC?
		7.4.5	INTEGRATION SCHEME
		7.4.6	CHOOSE THE ELEMENTS IN RELATION TO THE SOLUTION
		7.4.7	RULES FOR SELECTING THE RIGHT ELEMENTS
	7.5	SHEAR LOCKING
		7.5.1	WHAT IS SHEAR LOCKING?
		7.5.2	HOW TO PREVENT SHEAR LOCKING
	7.6	HOURGLASSING
		7.6.1	WHAT IS HOURGLASSING?
		7.6.2	HOW TO PREVENT HOURGLASSING
	7.7	EXAMPLES
		7.7.1	QUADRILATERAL ELEMENTS VS TRIANGULAR ELEMENTS
		7.7.2	HIGHER ORDER TETRAHEDRAL ELEMENTS VS LOWER ORDER ELEMENTS (TET10 VS TET4)
		7.7.3	EFFECT OF THE INTEGRATION SCHEME ON SHEAR LOCKING AND HOURGLASSING
Chapter 8	MESHING
	8.1	OVERVIEW
	8.2	UNDERSTANDING ELEMENT BEHAVIOR
	8.3	PLANNING THE MESHING
		8.3.1	STUDY THE GEOMETRY IN DETAIL
		8.3.2	CLEAN UP THE GEOMETRY
		8.3.3	SELECT THE ELEMENT TYPES
	8.4	SELECTING THE ELEMENT SIZE
		8.4.1	FACTORS THAT INFLUENCE MESH SIZE
		8.4.2	DEFLECTION, STIFFNESS, OR STRESS?
		8.4.3	PREDICT AND MATCH THE DEFORMED SHAPE
		8.4.4	MESHING OF CRITICAL REGIONS
		8.4.5	KEEP IT SIMPLE WHEN THE DESIGN IS NOT MATURE
	8.5	HOW TO DO MESH REFINEMENT
		8.5.1	WHY DO MESH REFINEMENT?
		8.5.2	THE MESH REFINEMENT PROCESS
		8.5.3	ADVANTAGES AND DISADVANTAGES OF MESH REFINEMENT
		8.5.4	EXAMPLES OF MESH REFINEMENT TECHNIQUES
		8.5.5	CONVERGENCE STUDY METHODOLOGY
		8.5.6	 OVER WHAT DISTANCE IS THE MESH REFINED?
		8.5.7	CAN YOU USE AN EXISTING CONVERGENCE STUDY IN OTHER MODELS?
		8.5.8	THE DIFFERENT MESH REFINEMENT METRICS
		8.5.9	CONVERGENCE STUDY GUIDELINES
		8.5.10	EXAMPLE OF A CONVERGENCE STUDY
	8.6	WHAT IS A PHYSICAL INTERFACE?
	8.7	WHAT ARE THE PREFERRED SHAPES FOR 2D AND 3D MODELS?
	8.8	HOW TO DO A MESH TRANSITION
		8.8.1	MESH TRANSITION USING VARIOUS ELEMENT TYPES
		8.8.2	MESH TRANSITION USING HIGHER ORDER ELEMENTS
		8.8.3	MESH TRANSITION BETWEEN DISSIMILAR ELEMENT TYPES
	8.9	1D MESHING RULES
	8.10	2D MESHING RULES
		8.10.1	WHY MESH IN 2D INSTEAD OF 3D?
		8.10.2	THE MID-PLANE CONCEPT
		8.10.3	THE TWO RULES OF MID-PLANE CREATION
		8.10.4	VARIABLE THICKNESS
		8.10.5	COMPARISON BETWEEN LINEAR AND QUADRATIC ELEMENTS
		8.10.6	RULES FOR MODELING HOLES AND FILLETS
		8.10.7	HOW TO CHECK A 2D MESH
		8.10.8	THE FOUR MOST COMMON 2D MESHING ERRORS
		8.10.9	HOW TO IMPROVE YOUR 2D MESH QUALITY
		8.10.10 OTHER RECOMMENDATIONS FOR 2D MESHING
	8.11	3D MESHING RULES
		8.11.1	TETRAHEDRAL MESHING TECHNIQUES
		8.11.2	RECOMMENDATIONS FOR TETRAHEDRAL MESHING
		8.11.3	LINEAR VS QUADRATIC TETRAHEDRAL ELEMENTS
		8.11.4	HOW TO CHECK A TETRAHEDRAL MESHING
		8.11.5	HEXAHEDRAL MESHING TECHNIQUES
		8.11.6	HOW TO CHECK HEXAHEDRAL MESHING
		8.11.7	ARE YOU ACTUALLY FACED WITH A 3D PROBLEM?
Chapter 9	SETTING YOUR UNITS
	9.1	CONSISTENT SYSTEMS OF UNITS
	9.2	THE MASS PROBLEM
	9.3	WEIGHT AND MASS DENSITY OF COMMON MATERIALS
	9.4	ENGINEERING UNITS FOR COMMON VARIABLES
Chapter 10  MATERIAL MODELING
	10.1	OVERVIEW
	10.2	ISOTROPIC MATERIAL
		10.2.1	DEFINING AN ISOTROPIC MATERIAL
		10.2.2	STRESS AND STRAIN
		10.2.3	STRESS-STRAIN CURVE
		10.2.4	PLASTIC AND ELASTIC STRAIN
		10.2.5	STRAIN HARDENING
		10.2.6	STRESS-STRAIN CURVE USING THE RAMBERG-OSGOOD MODEL
		10.2.7	STRESS-STRAIN CURVE USING THE HOLLOMON MODEL
		10.2.8	TRUE STRESS AND STRAIN
		10.2.9	SUMMARY OF THE TYPICAL BEHAVIORS OF METALLIC MATERIALS
	10.3	TWO-DIMENSIONAL ORTHOTROPIC MATERIAL
	10.4	TWO-DIMENSIONAL ANISOTROPIC MATERIAL
	10.5	THREE-DIMENSIONAL ANISOTROPIC MATERIAL
	10.6	THREE-DIMENSIONAL ORTHOTROPIC MATERIAL
Chapter 11 DEFINING LOADS AND BOUNDARY CONDITIONS
	11.1	OVERVIEW
	11.2	WHAT IS A BOUNDARY CONDITION?
	11.3	WHY DO WE NEED BOUNDARY CONDITIONS?
	11.4	WHAT ROLE DO BOUNDARY CONDITIONS PLAY?
	11.5	THE DIFFERENT TYPES OF BOUNDARY CONDITIONS
	11.6	USING BOUNDARY CONDITIONS TO CONSTRAIN A MODEL
		11.6.1	WHAT IS RIGID BODY MODE?
		11.6.2	WHAT IS A MECHANISM?
		11.6.3	HOW TO DETECT MECHANISMS IN AN FEA
		11.6.4	CONSTRAINT TYPES
		11.6.5 WHAT ARE SINGLE-POINT CONSTRAINTS?
		11.6.6	EXAMPLES OF CONSTRAINTS FOR 2D AND 3D PROBLEMS
		11.6.7	COMPATIBILITY OF BOUNDARY CONDITIONS WITH ELEMENTS
		11.6.8	CONSTRAINTS AND ENFORCED DISPLACEMENT
		11.6.9	HOW TO USE BOUNDARY CONDITIONS TO MODEL SYMMETRY AND ANTI-SYMMETRY
	11.7	INFLUENCE OF BOUNDARY CONDITIONS ON A SIMPLE PLATE MODEL
	11.8	USING BOUNDARY CONDITIONS TO SIMPLIFY A PROBLEM
	11.9	STRATEGY FOR PROPERLY DEFINING BOUNDARY CONDITIONS
		11.9.1	BOUNDARY CONDITIONS ARE NEVER PERFECT
		11.9.2	THE SEVEN QUESTIONS YOU SHOULD ANSWER TO SUCCESSFULLY DEFINE BOUNDARY CONDITIONS
		11.9.3	STRATEGY
	11.10	HOW TO CREATE ISOSTATIC RESTRAINTS
	11.11	THE OVER-STIFFENING AND UNDER-STIFFENING PROBLEM
		11.11.1 OVER-STIFFENING
		11.11.2 UNDER-STIFFENING
	11.12	HOW TO AVOID SINGULARITIES
		11.12.1 WHAT IS A SINGULARITY?
		11.12.2 RULES FOR AVOIDING SINGULARITIES
	11.13	ABOUT SUPPORT STIFFNESS
	11.14	HOW TO LOAD A MODEL
		11.14.1 LOADING TYPES
Chapter 12  RIGID BODY ELEMENTS AND MULTI-POINT CONSTRAINTS
	12.1	OVERVIEW
	12.2	TERMINOLOGY
	12.3	R-TYPE ELEMENTS
		12.3.1	INTRODUCTION TO R-TYPE ELEMENTS
		12.3.2	SMALL DISPLACEMENT THEORY
		12.3.3	TWO-NODE RIGID ELEMENT
		12.3.4	N-NODE RIGID ELEMENT
		12.3.5	INTERPOLATION ELEMENT
		12.3.6	R-TYPE ELEMENT SUMMARY
	12.4	MULTI-POINT CONSTRAINTS
		12.4.1 DEFINITION
		12.4.2	 SET UP AN MPC
		12.4.3 EXAMPLE 1: CREATE A DISPLACEMENT EQUALITY RELATIONSHIP ON A PER DEGREE OF FREEDOM LEVEL
		12.4.4 EXAMPLE 2: COMPUTE RELATIVE DISPLACEMENT
		12.4.5 EXAMPLE 3: ENFORCE A SEPARATION BETWEEN NODES
		12.4.6 EXAMPLE 4: AVERAGE MOTION
		12.4.7 EXAMPLE 5: CREATE A LINEAR CONTACT BETWEEN NODES
		12.4.8 EXAMPLE 6: CREATE A PRELOAD IN A 3D BOLT
		12.4.9 KEY POINTS OF THE MPC
Chapter 13  MODELING BOLTED JOINTS
	13.1	OVERVIEW
	13.2	DO YOU REALLY NEED TO MODEL THE BOLTS?
	13.3	THE VARIOUS FINITE ELEMENT MODELING APPROACHES FOR BOLTED JOINTS
		13.3.1	FASTENERS MODELED WITH RIGID ELEMENTS
		13.3.2	FASTENERS MODELED WITH DISCRETE SPRING ELEMENTS
		13.3.3	FASTENERS MODELED WITH BEAM ELEMENTS
		13.3.4	FASTENERS MODELED WITH CONNECTORS
		13.3.5	FASTENERS MODELED WITH THE RUTMAN METHOD
	13.4	HOW TO CALCULATE THE SPRING FASTENER STIFFNESS
		13.4.1	WHY CALCULATE THE FASTENER STIFFNESS?
		13.4.2	AXIAL STIFFNESS
		13.4.3	SHEAR STIFFNESS
		13.4.4	BENDING STIFFNESS
		13.4.5	TORSIONAL STIFFNESS
	13.5	HOW TO CONNECT THE FASTENER ELEMENTS TO THE SURROUNDING MESH
		13.5.1	CONNECT THE FASTENER WHEN THE HOLE IS MODELED
		13.5.2	CONNECT THE FASTENER WHEN THE HOLE IS NOT MODELED
	13.6	HOW TO CAPTURE THE PRYING EFFECT IN A BOLTED JOINT MODELED WITH A 1D SPRING
	13.7	PIN JOINT MODELING APPROACH
	13.8	BOLT PRELOAD
		13.8.1	PRELOAD IN A 1D BOLT
		13.8.2	PRELOAD IN A 3D BOLT
	13.9	DISCUSSION
Chapter 14 MODELING CONTACT
	14.1	OVERVIEW
	14.2	WHAT IS A CONTACT?
		14.2.1	INTRODUCTION
		14.2.2	DEFINITIONS
		14.2.3	CONTACT STRATEGY
		14.2.4	CONTACT FORCE
		14.2.5	FRICTION FORCE
		14.2.6	LINEAR OR NONLINEAR?
	14.3	CONTACT TYPES
		14.3.1	POINT-TO-POINT LINEAR CONTACT
		14.3.2	POINT-TO-POINT NONLINEAR CONTACT
		14.3.3	GENERAL CONTACT
	14.4	CONTACT ANALYSIS PROCEDURE
		14.4.1	THE TWO TYPES OF CONTACT INTERACTION
		14.4.2	THE TWO TYPES OF CONTACT BODY
		14.4.3	THE MASTER-SLAVE CONCEPT
		14.4.4	CONTACT DETECTION
		14.4.5	CONTACT TOLERANCE AND DETECTION ALGORITHMS
		14.4.7	SPECIFY THE CONTACT BETWEEN BODIES
		14.4.6	INFLUENCE OF THE LOAD INCREMENT ON CONTACT DETECTION
	14.5	GUIDELINES FOR DEFINING CONTACT
		14.5.1	KEEP IT SIMPLE IN THE BEGINNING
		14.5.2	DO NOT VARY THE MESH DENSITY VERY MUCH
		14.5.3	PAY ATTENTION TO THE RIGID-DEFORMABLE CONTACT
		14.5.4	MESH REQUIREMENTS
		14.5.5	PENALTY-BASED CONTACT METHOD
		14.5.6	PREVENTING RIGID BODY MOTION IN CONTACT SIMULATIONS
		14.5.7	ISOLATE THE PROBLEMS
		14.5.8	INITIAL CONTACT
		14.5.9	AVOID CRACKS IN THE CONTACT SURFACES
		14.5.10 CONTACT AT CORNERS
		14.5.11 MPCS INVOLVED IN CONTACT SURFACES
		14.5.12 SELF-CONTACT
	14.6	DO YOU REALLY NEED TO REPRESENT CONTACT IN YOUR SIMULATION?
		14.6.1	ARE THERE BODIES IN CONTACT IN YOUR MODEL?
		14.6.2	CAN A BODY TOUCH A RIGID SUPPORT IN THE MODEL?
		14.6.3	IS THERE AN INITIAL CONTACT?
		14.6.4	CAN YOU PREDICT WHERE THE CONTACT WILL BE?
	14.7	EXAMPLES
		14.7.1	POINT-TO-POINT LINEAR CONTACT BETWEEN TWO NODES
		14.7.2	POINT-TO-POINT LINEAR CONTACT ON A GROUNDED SURFACE
		14.7.3	POINT-TO-POINT NONLINEAR CONTACT
		14.7.4	GLUED CONTACT
		14.7.5	TOUCHING CONTACT
		14.7.6	CONTACT BETWEEN DEFORMABLE BODIES
		14.7.7	DEFORMABLE-RIGID CONTACT
Chapter 15 SUBMODELING
	15.1	WHAT IS SUBMODELING?
	15.2	WHY DO SUBMODELING?
	15.3	HOW TO DO SUBMODELING
		15.3.1	SUBMODEL A GLOBAL FEM
		15.3.2	EXTRACT A PART OF THE GLOBAL FEM
	15.4	TIPS AND HINTS FOR SUBMODELING
	15.5	DISPLACEMENT-BASED SUBMODELING VS FORCE-BASED SUBMODELING
	15.6	STATIC CONDENSATION
		15.6.1	FROM FEM TO MATRIX
		15.6.2	TERMINOLOGY AND STATIC CONDENSATION CONCEPT
		15.6.3	THE STATIC CONDENSATION PROCESS
		15.6.4	STATIC CONDENSATION VALIDATION
		15.6.5	LIMITATIONS OF THE STATIC CONDENSATION PROCESS
	15.7	EXAMPLES OF SUBMODELING
		15.7.1	SUBMODELING A GLOBAL FEM
		15.7.2	SUBMODELING BY EXTRACTING A COMPONENT FROM THE GLOBAL FEM
		15.7.3	SUBMODELING BY STATIC CONDENSATION
Chapter 16 VALIDATING AND CORRELATING YOUR FEA
	16.1	OVERVIEW
	16.2	ACCURACY CHECKS
	16.3	MATHEMATICAL VALIDITY CHECKS
		16.3.1	BASIC CONCEPTS FOR UNDERSTANDING MATHEMATICAL CHECKS
		16.3.2	MATHEMATICAL VALIDITY CHECK 1: FREE-FREE MODAL CHECK
		16.3.3	MATHEMATICAL VALIDITY CHECK 2: UNIT GRAVITY CHECK
		16.3.4	MATHEMATICAL VALIDITY CHECK 3: UNIT ENFORCED DISPLACEMENT CHECK
		16.3.5	MATHEMATICAL VALIDITY CHECK 4: THERMAL EQUILIBRIUM CHECK
	16.4	DEFORMATION CHECK
	16.5	HOW ACCURATE ARE THE HOT SPOTS?
	16.6	CORRELATION
		16.6.1	OBJECTIVE
		16.6.2	STRAIN GAUGE MEASUREMENTS
		16.6.3	TAP TESTING
		16.6.4	VALIDATION FACTORS AND CORRELATION PLOT
	16.7	MODEL CHECKOUT DOCUMENTATION
	16.8	MATHEMATICAL VALIDITY CHECK EXAMPLE
		16.8.1	EXAMPLE INTRODUCTION
		16.8.2	FREE-FREE MODAL CHECK
		16.8.3	UNIT GRAVITY CHECK
		16.8.4	UNIT ENFORCED DISPLACEMENT CHECK
Chapter 17 UNDERSTANDING FEA OUTPUTS
	17.1	OVERVIEW
	17.2	STANDARD OUTPUTS
		17.2.1	DEFORMED SHAPES
		17.2.2	ELEMENT FORCE
		17.2.3	STRESSES IN ELEMENTS
		17.2.4	PRINCIPAL STRESS OR VON MISES STRESS?
		17.2.5	FORCES AT BOUNDARY CONDITIONS
		17.2.6	FREE BODY DIAGRAM
	17.3	THE BASIC RULES OF POST-PROCESSING
		17.3.1	ANIMATE THE DISPLACEMENT FIRST
		17.3.2	CONTOUR PLOTS
		17.3.3	SELECT THE APPROPRIATE STRESS PLOT
		17.3.4	EXTRAPOLATION
		17.3.5	SELECT THE APPROPRIATE TYPE OF STRESS
		17.3.6	DO NOT NEGLECT THE CONVERGENCE TEST
		17.3.7	VALIDATE THE LINEAR ASSUMPTION
		17.3.8	DO NOT CONFUSE FORCES AND FLOWS FOR 2D SHELL ELEMENTS
		17.3.9	PAY ATTENTION TO COORDINATE SYSTEMS
		17.3.10 ADJUSTING THE SCALE OF THE COLOR BAR
		17.3.11 REPORT THE MAXIMUM STRESS LOCATION
		17.3.12 TOP AND BOTTOM STRESSES FOR 2D SHELL ELEMENTS
		17.3.13 GRAPH THE RESULTS
		17.3.14 INTERPRETATION OF RESULTS AND DESIGN MODIFICATIONS
		17.3.15 EXPORT THE RESULTS IN REPORTS
		17.3.16 USE THE READING ELEMENTS
		17.3.17 VECTOR PLOT
	17.4	HOW TO DEAL WITH SINGULARITIES
		17.4.1	ARE YOU INTERESTED IN RESULTS AROUND A SINGULARITY?
		17.4.2	IMPACT OF A SINGULARITY
		17.4.3	CAN I IGNORE SINGULARITIES?
		17.4.4	HOW DO I AVOID A SINGULARITY DUE TO A POINT LOADING?
Chapter 18 IMPROVING YOUR PERFORMANCE COMPUTING
	18.1	OVERVIEW
	18.2	CPU POWER AND CLOCK SPEED
	18.3	MEMORY SIZE
	18.4	CACHE SIZE
	18.5	HARD DRIVE SPEED
	18.6	PARALLEL COMPUTING
		18.6.1	OVERVIEW
		18.6.2	PARALLEL COMPUTER ARCHITECTURES: SMP VS DMP
		18.6.3	THE BASICS OF HIGH-PERFORMANCE COMPUTING (HPC)
	18.7	WAYS TO SPEED UP YOUR SIMULATIONS
		18.7.1	SYSTEM OPTIMIZATION
		18.7.2	MANAGE MEMORY
		18.7.3	OPTIMIZE THE OUTPUT REQUESTS
		18.7.4	MAKE USE OF MULTIPLE CORES (SMP)
		18.7.5	ABOUT HYPER-THREADING
Chapter 19	 DOCUMENTING YOUR FEA
	19.1	OVERVIEW
	19.2	MODEL DESCRIPTION
	19.3	GEOMETRY SOURCE
	19.4	MODEL ASSUMPTIONS
	19.5	SIMULATION PARAMETERS
	19.6	VERIFICATION AND VALIDATION
Chapter 20	 LINEAR STATIC ANALYSIS
	20.1	OVERVIEW
	20.2	WHAT IS LINEAR STATIC ANALYSIS?
	20.3	HOW TO SOLVE A LINEAR STATIC PROBLEM
	20.4	CHARACTERISTICS OF A LINEAR ANALYSIS
		20.4.1	LOAD-DISPLACEMENT RELATION
		20.4.2	STRESS-STRAIN RELATION
		20.4.3	SCALABILITY
		20.4.4	SUPERPOSITION
		20.4.5	REVERSIBILITY AND LOAD HISTORY
		20.4.6	SOLUTION SETTINGS
	20.5	EXAMPLES OF LINEAR STATIC ANALYSIS
		20.5.1	CHARACTERISTICS OF A LINEAR STATIC ANALYSIS
		20.5.2	HOW DOES MATERIAL AFFECT STRESS IN A LINEAR STATIC SOLUTION?
Chapter 21	 NONLINEAR STATIC ANALYSIS
	21.1	OVERVIEW
	21.2	WHAT IS A NONLINEAR SYSTEM?
	21.3	CHARACTERISTICS OF A NONLINEAR ANALYSIS
		21.3.1	LOAD-DISPLACEMENT RELATION
		21.3.2	STRESS-STRAIN RELATION
		21.3.3	SCALABILITY
		21.3.4	SUPERPOSITION
		21.3.5	INITIAL STATE OF STRESS
		21.3.6	LOAD HISTORY
		21.3.7	REVERSIBILITY
		21.3.8	SOLUTION SETTINGS
	21.4	GEOMETRIC NONLINEARITY
		21.4.1	SOURCES OF GEOMETRICAL NONLINEARITY
		21.4.2	HOW DOES NONLINEAR GEOMETRY WORK?
		21.4.3	DO YOU REALLY NEED A NONLINEAR GEOMETRIC ANALYSIS?
		21.4.4	THE FOLLOWER LOAD CONCEPT
		21.4.5	SMALL OR LARGE STRAIN?
		21.4.6	EXAMPLE OF GEOMETRIC NONLINEARITY
	21.5	MATERIAL NONLINEARITY
		21.5.1	YIELD CRITERIA
		21.5.2	HARDENING RULES
		21.5.3	MATERIAL MODELS
		21.5.4	ENGINEERING STRESS-STRAIN OR TRUE STRESS-STRAIN?
		21.5.5	HOW DOES NONLINEAR MATERIAL WORK?
		21.5.6	DO YOU REALLY NEED A NONLINEAR MATERIAL ANALYSIS?
	21.6	BOUNDARY NONLINEARITY
		21.6.1	LOAD VARIATION
		21.6.2	CONSTRAINT VARIATION
		21.6.3	CONTACTS
	21.7	CHOOSING THE RIGHT ELEMENTS FOR A NONLINEAR ANALYSIS
	21.8	HOW DO FEA SOFTWARE COMPUTE NONLINEAR PROBLEMS?
		21.8.1	CHARACTERIZATION AND FORMULATION OF A NONLINEAR PROBLEM
		21.8.2	NEWTON-RAPHSON METHOD
		21.8.3	MODIFIED NEWTON-RAPHSON METHOD
		21.8.4	NEWTON-RAPHSON METHOD EXAMPLES
		21.8.5	COMPUTATIONAL METHODS IN NONLINEAR ANALYSIS
		21.8.6	EQUILIBRIUM PATH AND CRITICAL POINTS
		21.8.7	ADAPTIVE SOLUTION STRATEGIES
		21.8.8	STIFFNESS MATRIX UPDATE STRATEGIES
		21.8.9	CHOOSING THE INCREMENTAL LOAD STEP
		21.8.10 ARC-LENGTH METHODS
		21.8.11 LINE SEARCH PROCEDURES
		21.8.12 CONVERGENCE CRITERIA
		21.8.13 HOW TO DEAL WITH CONVERGENCE ISSUES
		21.8.14 SUMMARY OF ITERATIVE SOLUTION SCHEMES
		21.8.15 HOW TO SELECT THE RIGHT ITERATIVE SOLUTION SCHEME
		21.8.16 SUMMARY OF THE NONLINEAR SOLUTION STRATEGY
	21.9	GENERAL RECOMMENDATIONS FOR NONLINEAR ANALYSIS
		21.9.1	UNDERSTAND THE NONLINEAR FEATURES
		21.9.2	UNDERSTAND YOUR PROBLEM AND STRUCTURAL BEHAVIOR
		21.9.3	UNDERSTAND THE DIFFERENCE BETWEEN A LINEAR SUBCASE AND A NONLINEAR SUBCASE
		21.9.4	SIMPLIFY YOUR MODEL
		21.9.5	USE AN ADEQUATE MESH AND ELEMENT TYPES
		21.9.6	APPLY LOADING GRADUALLY
		21.9.7	READ THE OUTPUT
		21.9.8	NUMBER OF INCREMENTS
		21.9.9	CONVERGENCE PROBLEMS
		21.9.10 KEEP AN EYE ON YOUR MATERIAL DEFINITION
	21.10	COMMON MISTAKES IN NONLINEAR ANALYSIS
	21.11	EXAMPLES OF NONLINEAR STATIC ANALYSIS
		21.11.1 GEOMETRIC NONLINEARITY AND HISTORY PATH
		21.11.2 CUMULATIVE EFFECT OF A NONLINEAR ANALYSIS
		21.11.3 INFLUENCE OF THE INCREMENTAL LOAD STEP ON RESULTS
		21.11.4 MATERIAL NONLINEARITY: ELASTOPLASTIC PLATE
		21.11.5 HIGHLY NONLINEAR PROBLEM
Chapter 22 LINEAR BUCKLING ANALYSIS
	22.1	WHAT IS LINEAR BUCKLING ANALYSIS?
	22.2	ASSUMPTIONS AND LIMITATIONS OF LINEAR BUCKLING ANALYSIS
	22.3	LINEAR BUCKLING ANALYSIS OUTCOMES
	22.4	HOW DO SOLVERS COMPUTE LINEAR BUCKLING PROBLEMS?
		22.4.1	THE EQUATION OF MOTION WITH DIFFERENTIAL STIFFNESS MATRIX
		22.4.2	HOW TO COMPUTE THE EIGEN EQUATION
		22.4.3	SOLUTION OF THE BUCKLING PROBLEM
	22.5	THE LINEAR BUCKLING STRATEGY
		22.5.1	EVERYTHING STARTS WITH A LINEAR STATIC ANALYSIS
		22.5.2	SELECT YOUR BUCKLING CASES
		22.5.3	MESHING HINTS
	22.6	EXAMPLES OF LINEAR BUCKLING ANALYSIS
		22.6.1	EULER BEAM BUCKLING
		22.6.2	PANEL BUCKLING
		22.6.3	STIFFENED PANEL BUCKLING
		22.6.4	INFLUENCE OF MESHING DENSITY ON BUCKLING PREDICTIONS
Chapter 23 NONLINEAR BUCKLING ANALYSIS
	23.1	OVERVIEW
	23.2	WHY PERFORM A NONLINEAR BUCKLING ANALYSIS?
	23.3	THE STABILITY PATH AND THE CONVERGED SOLUTION
	23.4	NONLINEAR BUCKLING PROCEDURE
	23.5	POST-BUCKLING
	23.6	ESSENTIAL STEPS IN NONLINEAR BUCKLING ANALYSIS
	23.7	EXAMPLES OF NONLINEAR BUCKLING ANALYSIS
		23.7.1	NONLINEAR BUCKLING OF A CURVED PANEL
		23.7.2	SNAP-THROUGH: NEWTON-RAPHSON VS ARC-LENGTH
Chapter 24 NORMAL MODE ANALYSIS
	24.1	OVERVIEW
	24.2	HOW TO SOLVE THE REAL EIGENVALUE PROBLEM
		24.2.1	THE EQUATION OF MOTION
		24.2.2	HOW TO COMPUTE THE EIGEN EQUATION
		24.2.3	SOLUTION OF THE EIGEN EQUATION
		24.2.4	EIGENVALUE EXTRACTION METHOD
	24.3	WHAT A MODE IS AND WHAT IT IS NOT
		24.3.1	NATURAL FREQUENCIES
		24.3.2	WHAT A MODE IS
		24.3.3	WHAT A MODE IS NOT
	24.4	HOW ARE NATURAL FREQUENCIES AND MODE SHAPES INFLUENCED?
	24.5	WHY COMPUTE A MODAL ANALYSIS?
		24.5.1	FINDING WEAKNESSES IN A MODEL
		24.5.2	AVOID RESONANCE
	24.6	EXAMPLES OF MODAL ANALYSIS
		24.6.1	MODEL CHECKS
		24.6.2	FIND THE NATURAL FREQUENCIES TO AVOID RESONANCE
		24.6.3	EVALUATE THE MODAL EFFECTIVE MASS
		24.6.4	INFLUENCE OF THE PRE-STIFFNESS ON THE NATURAL FREQUENCIES
Chapter 25 GOOD MODELING PRACTICES
	25.1	OVERVIEW
	25.2	GOOD MODELING PRACTICES APPROACH
	25.3	IT ALL STARTS WITH A GOOD PLAN
	25.4	UNDERSTAND THE PROBLEM TO ANALYZE IN DETAIL
	25.5	DEFINE YOUR DESIGN OBJECTIVE
	25.6	BE SURE OF THE INPUTS AND REQUIREMENTS
	25.7	SELECT THE RIGHT TYPE OF ANALYSIS
	25.8	CLEAN UP THE GEOMETRY
	25.9	CHECK THE GEOMETRY
	25.10	SELECT THE PROPER ELEMENTS
	25.11	CREATE AN INTELLIGIBLE MESH
	25.12	DEFINE THE RIGHT BOUNDARY CONDITIONS
	25.13	VALIDATE THE INPUT DATA
	25.14	DEFINE CONTACT PROPERLY
	25.15	MODEL THE RIGHT MATERIAL BEHAVIOR
	25.16	MANAGE THE UNITS
	25.17	SHOULD YOU MODEL THE ENTIRE STRUCTURE?
	25.18	MANAGE THE SINGULARITIES
	25.19	SHOULD YOU MODEL THE BOLTS?
	25.20	MANAGE INCOMPATIBLE DEGREES OF FREEDOM
	25.21	KEEP AN EYE ON THE SOLUTION’S PARAMETERS
	25.22	VERIFY AND VALIDATE YOUR MODEL
	25.23	READ THE SOLVER’S MESSAGES
	25.24	KEEP A CRITICAL EYE ON THE RESULTS
	25.25	DOCUMENT EVERYTHING
	25.26	ASK FOR HELP
	25.27	THE MOST COMMON MISTAKES IN FEA
	25.28	THE 10 COMMANDMENTS OF THE FEA ANALYST
GLOSSARY AND ABBREVIATIONS
REFERENCES
IMAGE CREDITS
INDEX
QUOTE
ABOUT THE BOOK AND THE AUTHOR
TESTIMONIAL